Column I, Column II Collinear vectors, p.` vec a` Coinitial vectors, q. ` vec b` Equal vectors, r. ` vec c` Unlike vectors (same intitial point), s. ` vec d`

For given vector, vec a = 2 hat i j +2 hat k and vec b = - hat i + hat j - hat k , find the unit vector in the direction of the vector vec a + vec b .

If vec a , a n d vec b are unit vectors , then find the greatest value of | vec a+ vec b|+| vec a- vec b|dot

If vec a , vec b are two non-collinear vectors, prove that the points with position vectors vec a+ vec b , vec a- vec b and vec a+lambda vec b are collinear for all real values of lambdadot

Column I, Column II If | vec a+ vec b|=| vec a+2 vec b| , then angel between vec aa n d vec b is, p. 90^0 If | vec a+ vec b|=| vec a-2 vec b| , then angel between vec aa n d vec b is, q. obtuse If | vec a+ vec b|=| vec a- vec b| , then angel between vec aa n d vec b is, r. 0^0 Angle between vec axx vec b and a vector perpendicular to the vector vec cxx( vec axx vec b) is, s. acute

Given two vectors vec a=- hat i+2 hat j+2 hat ka n d vec b=-2 hat i+ hat j+2 hat kdot Column I, Column II A vector coplanar with vec aa n d vec b , p. -3 hat i+3 hat j+4 hat k A vector which is perpendicular to both vec aa n d vec b , q. 2 hat i-2 hat j+3 hat k A vector which is equally inclined to vec aa n d vec b , r. hat i+ hat j A vector which forms a triangle with vec aa n d vec b , s. hat i- hat j+5 hat k

If vec a , vec b ,a n d vec c are non-zero vectors such that vec a. vec b= vec a. vec c , then find the geometrical relation between the vectors.

The position vectors of the vertices A ,Ba n dC of a triangle are three unit vectors vec a , vec b ,a n d vec c , respectively. A vector vec d is such that vec d ⋅ vec a = vec d ⋅ vec b = vec d ⋅ vec c a n d vec d=lambda( vec b+ vec c)dot Then triangle A B C is a. acute angled b. obtuse angled c. right angled d. none of these

The scalars l and m such that l vec a+m vec b= vec c ,where vec a , vec b and vec c are given vectors, are equal to

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

For any four vectors, vec a , vec b , vec c and vec d prove that vec d.( vec axx( vec bxx( vec cxx vec d)))=( vec b. vec d)[ vec a \ vec c \ vec d] .